Sr Examen
Integral de dx/(3sinx+4cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------- dx | 3*sin(x) + 4*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx$$
Integral(1/(3*sin(x) + 4*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / /x\\ /1 /x\\ | log|-2 + tan|-|| log|- + tan|-|| | 1 \ \2// \2 \2// | ------------------- dx = C - ---------------- + --------------- | 3*sin(x) + 4*cos(x) 5 5 | /
$$\int \frac{1}{3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 2 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{1}{2} \right)}}{5}$$
Gráfica
Respuesta
[src]
log(2 - tan(1/2)) log(1/2 + tan(1/2)) 2*log(2)
- ----------------- + ------------------- + --------
5 5 5
$$- \frac{\log{\left(2 - \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{\log{\left(\frac{1}{2} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{2 \log{\left(2 \right)}}{5}$$
=
=
log(2 - tan(1/2)) log(1/2 + tan(1/2)) 2*log(2)
- ----------------- + ------------------- + --------
5 5 5
$$- \frac{\log{\left(2 - \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{\log{\left(\frac{1}{2} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{2 \log{\left(2 \right)}}{5}$$
-log(2 - tan(1/2))/5 + log(1/2 + tan(1/2))/5 + 2*log(2)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.